Their son's unusual first name was a tribute to Omar D. Gray, a newspaper editor. [...] Speculating further, the newspaper editor's politics - a prominent part of his trade at the time - seem to have celebrated the common man against the big Eastern interests. John's [Omar's father] decision to give the editor's name to his son was as much a statement of values as it was a way to make him unique.

(From Omar Bradley: General at War, Jim DeFelice, p9; Google Books

That raises the question of why the newspaper editor in a small Missouri town had an Arab name, and I suspect no one knows the answer to that question.